A Linear-Expected-Time Algorithm for Sparse Random Instances of Max Cut and Other Max 2-CSP.
Speaker : Greg Sorkin
Audience Learner: CollegeLanguage EnglishAudio/Visual sound, color
Keywords : Analysis of algorithms; average-case analysis; branching processes; Brownian motion; phase transition; scaling window; constraint satisfaction; satisfiability.
Abstract : A maximum cut in a random graph below the giant component threshold can be found in linear space and linear expected time by a simple algorithm. The same algorithm solves the more general class Max 2-CSP of weighted binary 2-variable constraint satisfaction problems, which includes weighted Max Cut, Max Dicut and Max 2-Sat. For a semi-random instance of such a problem where the underlying graph is a random graph below or at the giant-component threshold and the constraints and weights are arbitrary, the same linear space and linear expected time bounds apply. Furthermore, our results are uniform through and above the scaling window. Arbitrary (non-random) instances with m constraints can be solved in time of order 2 to the power m/5.